'columns'=>array(
...
array(
'name' => 'user_id',
'header'=>'User',
'sortable'=>false, // since it would still be sorting based on ID
// 'value' => '$data->user->lastname', // basic version
'value'=>'CHtml::link((isset($data->user))?$data->user->username:$data->user_id,array("user/view","id"=>$data->user_id))', // link version
),

It's a fun little trick: if the search term is a string and NOT an intval(), it searches for the user by their secondname, via the "user" relation. But if you enter a user_id, it will find the user by their user_id - the default search() functionality.

NOTE: This will enable filtering, but it will still sort based on ID. You will need to implement something additional to get the sorting to work.

There are surely other ways to do this, but this is how I do it. I suspect there is a "right" to do this using the relation, but my technique works solid.